To determine where the function $f(x)$ is decreasing, we need to analyze the intervals where the graph has a downward slope, meaning $f(x)$ decreases as $x$ increases. This is typically seen where the graph moves down from left to right.

Step-by-Step Analysis

1. Identify Decreasing Intervals on the Graph:

   • From the image, observe that the graph of $f(x)$ decreases on two specific intervals:
     • Starting from the left, it decreases from approximately $x = -\infty$ to around $x = -2$.
     • The graph also decreases from approximately $x = 1$ to $x = 4$.

2. Conclusion:

   • Therefore, the intervals where $f(x)$ is decreasing are: $(-\infty, -2) \quad \text{and} \quad (1, 4).$

Would you like more details on how to find these intervals or have any questions?

Related Questions for Practice

1. How do you determine where a function is increasing on an interval?
2. What is the significance of critical points in finding increasing or decreasing intervals?
3. How does the derivative of a function help identify increasing and decreasing intervals?
4. What would change in the intervals if the graph was shifted up or down?
5. How can you tell if a function is constant over an interval?

Tip

To verify decreasing intervals analytically, take the derivative of $f(x)$ and identify where $f'(x) < 0$.